There is a solution. Starting from C−1(A+X)B−1=In C−1(A+X)B−1=In, multiply both of the sides of the equation, by C and multiply both sides of the equation by B.
In other terms, this is the solution:
Given: C^(-1)(A + X)B^(-1) = In
= CC^(-1)(A + X)B^(-1)B = CInB
= In(A + X)In = CB
= AInIn + XInIn = CB
= A + X = CB
X = CB – A
The final answer Is X = CB – A